Direct relationship
Encyclopedia
In mathematics
and statistics
, a positive or direct relationship is a relationship between two variables
in which change in one variable is associated with a change in the other variable in the same direction. For example all linear
relationships with a positive slope
are direct relationships. Such direct relationships are very widely used in science
and mathematics
.
In a direct relationship, as one variable, say x, increases, the other variable, say y, also increases, and if one variable decreases, the other variable decreases. The formula for a direct linear relation is
See for example temperature conversion, where two temperature scales are typically in a direct and linear relation.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, a positive or direct relationship is a relationship between two variables
Variable (mathematics)
In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...
in which change in one variable is associated with a change in the other variable in the same direction. For example all linear
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...
relationships with a positive slope
Slope
In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline....
are direct relationships. Such direct relationships are very widely used in science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
.
In a direct relationship, as one variable, say x, increases, the other variable, say y, also increases, and if one variable decreases, the other variable decreases. The formula for a direct linear relation is
- y = a + kx, where k is positive constant and a is a constant.
See for example temperature conversion, where two temperature scales are typically in a direct and linear relation.